Removing the ghost reflections from seismic data is for many experimental configurations equivalent to up/down wavefield separation of the recorded data. In such configurations the down-going part of the wavefield represents the ghost and the up-going wavefield represents the desired signal. Exact filters for up/down separation of multi-component wavefield measurements in Ocean Bottom Cable (OBC) configurations have been derived by Amundsen and Ikelle, and are described in U.K. Patent Application Number 9800741.2. An example of such a filter corresponding to de-ghosting of pressure data at a frequency of 50 Hz for a seafloor with P-velocity of 2000 m/s, S-velocity of 500 m/s and density of 1800 kg/m3 is shown in FIG. 2. At this frequency, the maximum horizontal wavenumber for P-waves right below the seafloor is k=0.157 m−1, whereas it is k=0.628 m−1 for S-waves. Notice the pole and the kink due to a zero in the filter at these two wavenumbers, making approximations necessary for robust filter implementations. FIG. 3 shows approximations co the filter. These filters are only good at wavenumbers smaller than the wavenumber where the pole occurs. Hence, energy with low apparent velocities (for instance S-waves or Scholte waves at the seafloor) will not be treated properly. Moreover, since they do not have a complex part, evanescent waves will also not be treated properly.
The OBC de-ghosting filters have been shown to work very well on synthetic data. However, apart from the difficulty with poles and zeros at critical wave numbers, they also require knowledge about the principles of the immediate sub-bottom locations as well as hydrophone/geophone calibration and coupling compensation.
A normal incidence approximation to the de-ghosting filters for data acquired at the sea floor was described by Barr, F. J. in U.S. Pat. No. 4,979,150,issued 1990, entitled ‘System for attenuating water-column reflections’, (hereinafter “Barr (1990)”). For all practical purposes, this was previously described by White, J. E., in a 1965 article entitled ‘Seismic waves: radiation, transmission and attenuation’, McGraw-Hill (hereinafter “White (1965)”). However, this technique is not effective when the angle of incidence is away from vertical. Also, this technique does not completely correct for wide-angle scattering and the complex reflections from rough sea surfaces. Additionally, its is believed that the OBC techniques described have not been used successfully in a fluid medium, such as with data gathered with towed streamers.